Learning Goals LG1 Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. LG2 Review the legal aspects of bond financing and bond cost. LG3 Discuss the general features, yields, prices, popular types, and international issues of corporate bonds. © 2012 Pearson Education

Learning Goals (cont.) LG4 Understand the key inputs and basic model used in the valuation process. LG5 Apply the basic valuation model to bonds and describe the impact of required return and time to maturity on bond values. LG6 Explain yield to maturity (YTM), its calculation, and the procedure used to value bonds that pay interest semiannually. © 2012 Pearson Education

Interest Rates and Required Returns: Interest Rate Fundamentals The interest rate is usually applied to debt instruments such as bank loans or bonds; the compensation paid by the borrower of funds to the lender; from the borrower’s point of view, the cost of borrowing funds. The required return is usually applied to equity instruments such as common stock; the cost of funds obtained by selling an ownership interest. © 2012 Pearson Education

Interest Rates and Required Returns: Interest Rate Fundamentals Several factors can influence the equilibrium interest rate: Inflation, which is a rising trend in the prices of most goods and services. Risk, which leads investors to expect a higher return on their investment Liquidity preference, which refers to the general tendency of investors to prefer short-term securities © 2012 Pearson Education

Interest Rates and Required Returns: The Real Rate of Interest The real rate of interest is the rate that creates equilibrium between the supply of savings and the demand for investment funds in a perfect world, without inflation, where suppliers and demanders of funds have no liquidity preferences and there is no risk. The real rate of interest changes with changing economic conditions, tastes, and preferences. The supply-demand relationship that determines the real rate is shown in Figure 6.1 on the following slide. © 2012 Pearson Education

Figure 6.1 Supply–Demand Relationship © 2012 Pearson Education

Interest Rates and Required Returns: Nominal or Actual Rate of Interest (Return) The nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander. The nominal rate differs from the real rate of interest, r* as a result of two factors: Inflationary expectations reflected in an inflation premium (IP), and Issuer and issue characteristics such as default risks and contractual provisions as reflected in a risk premium (RP). © 2012 Pearson Education

Interest Rates and Required Returns: Nominal or Actual Rate of Interest (cont.) The nominal rate of interest for security 1, r1, is given by the following equation: The nominal rate can be viewed as having two basic components: a risk-free rate of return, RF, and a risk premium, RP1: r1 = RF + RP1 © 2012 Pearson Education

Interest Rates and Required Returns: Nominal or Actual Rate of Interest (cont.) For the moment, ignore the risk premium, RP1, and focus exclusively on the risk-free rate. The risk free rate can be represented as: RF = r* + IP The risk-free rate (as shown in the preceding equation) embodies the real rate of interest plus the expected inflation premium. The inflation premium is driven by investors’ expectations about inflation—the more inflation they expect, the higher will be the inflation premium and the higher will be the nominal interest rate. © 2012 Pearson Education

Personal Finance Example Marilyn Carbo has $10 that she can spend on candy costing $0.25 per piece. She could buy 40 pieces of candy ($10.00/$0.25) today. The nominal rate of interest on a 1-year deposit is currently 7%, and the expected rate of inflation over the coming year is 4%. © 2012 Pearson Education

Personal Finance Example If Marilyn invested the $10, how many pieces of candy could she buy in one year? In one year, Marilyn would have (1 + 0.07)  $10.00 = $10.70 Due to inflation, one piece of candy would cost (1 + 0.04)  $0.25 = $0.26 As a result, Marilyn would be able to buy $10.70/$0.26 = 41.2 pieces This 3% increase in buying power (41.2/40) is Marilyn’s real rate of return © 2012 Pearson Education

Figure 6.2 Impact of Inflation © 2012 Pearson Education

Term Structure of Interest Rates The term structure of interest rates is the relationship between the maturity and rate of return for bonds with similar levels of risk. A graphic depiction of the term structure of interest rates is called the yield curve. The yield to maturity is the compound annual rate of return earned on a debt security purchased on a given day and held to maturity. © 2012 Pearson Education

Figure 6.3 Treasury Yield Curves © 2012 Pearson Education

Term Structure of Interest Rates: Yield Curves (cont.) A normal yield curve is an upward-sloping yield curve indicates that long-term interest rates are generally higher than short-term interest rates. An inverted yield curve is a downward-sloping yield curve indicates that short-term interest rates are generally higher than long-term interest rates. A flat yield curve is a yield curve that indicates that interest rates do not vary much at different maturities. © 2012 Pearson Education

Term Structure of Interest Rates: Theories of Term Structure Expectations Theory Expectations theory is the theory that the yield curve reflects investor expectations about future interest rates; an expectation of rising interest rates results in an upward-sloping yield curve, and an expectation of declining rates results in a downward-sloping yield curve. © 2012 Pearson Education

Term Structure of Interest Rates: Theories of Term Structure (cont.) Expectations Theory (example) Suppose that a 5-year Treasury note currently offers a 3% annual return. Investors believe that interest rates are going to decline, and 5 years from now, they expect the rate on a 5-year Treasury note to be 2.5%. According to the expectations theory, what is the return that a 10-year Treasury note has to offer today? What does this imply about the slope of the yield curve? © 2012 Pearson Education

Term Structure of Interest Rates: Theories of Term Structure (cont.) Expectations Theory (example) Consider an investor who purchases a 5-year note today and plans to reinvest in another 5-year note in the future. Over the 10-year investment horizon, this investor expects to earn about 27.5%, ignoring compounding (that’s 3% per year for the first 5 years and 2.5% per year for the next 5 years). To compete with that return, a 10-year bond today could offer 2.75% per year. That is, a bond that pays 2.75% for each of the next 10 years produces the same 27.5% total return that the series of two, 5-year notes is expected to produce. Therefore, the 5-year rate today is 3% and the 10-year rate today is 2.75%, and the yield curve is downward sloping. © 2012 Pearson Education

Term Structure of Interest Rates: Theories of Term Structure (cont.) Liquidity Preference Theory Liquidity preference theory suggests that long-term rates are generally higher than short-term rates (hence, the yield curve is upward sloping) because investors perceive short-term investments to be more liquid and less risky than long-term investments. Borrowers must offer higher rates on long-term bonds to entice investors away from their preferred short-term securities. © 2012 Pearson Education

Term Structure of Interest Rates: Theories of Term Structure (cont.) Market Segmentation Theory Market segmentation theory suggests that the market for loans is segmented on the basis of maturity and that the supply of and demand for loans within each segment determine its prevailing interest rate; the slope of the yield curve is determined by the general relationship between the prevailing rates in each market segment. © 2012 Pearson Education

Risk Premiums: Issue and Issuer Characteristics © 2012 Pearson Education

Table 6.1 Debt-Specific Issuer- and Issue-Related Risk Premium Components © 2012 Pearson Education

Corporate Bonds A bond is a long-term debt instrument indicating that a corporation has borrowed a certain amount of money and promises to repay it in the future under clearly defined terms. The bond’s coupon interest rate is the percentage of a bond’s par value that will be paid annually, typically in two equal semiannual payments, as interest. The bond’s par value, or face value, is the amount borrowed by the company and the amount owed to the bond holder on the maturity date. The bond’s maturity date is the time at which a bond becomes due and the principal must be repaid. © 2012 Pearson Education

Corporate Bonds: Legal Aspects of Corporate Bonds The bond indenture is a legal document that specifies both the rights of the bondholders and the duties of the issuing corporation. Standard debt provisions are provisions in a bond indenture specifying certain record-keeping and general business practices that the bond issuer must follow; normally, they do not place a burden on a financially sound business. Restrictive covenants are provisions in a bond indenture that place operating and financial constraints on the borrower. These provisions help protect the bondholder against increases in borrower risk. Without them, the borrower could increase the firm’s risk but not have to pay increased interest to compensate for the higher risk. © 2012 Pearson Education

Corporate Bonds: Legal Aspects of Corporate Bonds (cont.) The most common restrictive covenants do the following: Require a minimum level of liquidity, to ensure against loan default. Prohibit the sale of accounts receivable to generate cash. Selling receivables could cause a long-run cash shortage if proceeds were used to meet current obligations. Impose fixed-asset restrictions. The borrower must maintain a specified level of fixed assets to guarantee its ability to repay the bonds. Constrain subsequent borrowing. Additional long-term debt may be prohibited, or additional borrowing may be subordinated to the original loan. Subordination means that subsequent creditors agree to wait until all claims of the senior debt are satisfied. Limit the firm’s annual cash dividend payments to a specified percentage or amount. © 2012 Pearson Education

Corporate Bonds: Legal Aspects of Corporate Bonds (cont.) A trustee is a paid individual, corporation, or commercial bank trust department that acts as the third party to a bond indenture and can take specified actions on behalf of the bondholders if the terms of the indenture are violated. © 2012 Pearson Education

Corporate Bonds: Cost of Bonds to the Issuer In general, the longer the bond’s maturity, the higher the interest rate (or cost) to the firm. In addition, the larger the size of the offering, the lower will be the cost (in % terms) of the bond (administration costs per dollar are to decrease) Also, the greater the default risk of the issuing firm, the higher the cost of the issue. Finally, the cost of money in the capital market is the basis form determining a bond’s coupon interest rate. © 2012 Pearson Education

Corporate Bonds: Bond Prices Because most corporate bonds are purchased and held by institutional investors, such as banks, insurance companies, and mutual funds, rather than individual investors, bond trading and price data are not readily available to individuals. Although most corporate bonds are issued with a par, or face, value of $1,000, all bonds are quoted as a percentage of par. A $1,000-par-value bond quoted at 94.007 is priced at $940.07 (94.007%  $1,000). Corporate bonds are quoted in dollars and cents. Thus, Company C’s price of 103.143 for the day was $1,031.43—that is, 103.143%  $1,000. © 2012 Pearson Education

Table 6.2 Data on Selected Bonds © 2012 Pearson Education

Table 6.3 Moody’s and Standard & Poor’s Bond Ratings © 2012 Pearson Education

Table 6.4a Characteristics and Priority of Lender’s Claim of Traditional Types of Bonds © 2012 Pearson Education

Table 6.4b Characteristics and Priority of Lender’s Claim of Traditional Types of Bonds © 2012 Pearson Education

Table 6.5 Characteristics of Contemporary Types of Bonds © 2012 Pearson Education

Corporate Bonds: International Bond Issues Companies and governments borrow internationally by issuing bonds in two principal financial markets: A Eurobond is a bond issued by an international borrower and sold to investors in countries with currencies other than the currency in which the bond is denominated. In contrast, a foreign bond is a bond issued in a host country’s financial market, in the host country’s currency, by a foreign borrower. Both markets give borrowers the opportunity to obtain large amounts of long-term debt financing quickly, in the currency of their choice and with flexible repayment terms. © 2012 Pearson Education

Valuation Fundamentals Valuation is the process that links risk and return to determine the worth of an asset. There are three key inputs to the valuation process: Cash flows (returns) Timing A measure of risk, which determines the required return © 2012 Pearson Education

Personal Finance Example Celia Sargent wishes to estimate the value of three assets she is considering investing in: Stock in Michaels Enterprises Expect to receive cash dividends of $300 per year indefinitely. Oil well Expect to receive cash flow of $2,000 at the end of year 1, $4,000 at the end of year 2, and $10,000 at the end of year 4, when the well is to be sold. Original painting Expect to be able to sell the painting in 5 years for $85,000. With these cash flow estimates, Celia has taken the first step toward placing a value on each of the assets. © 2012 Pearson Education

Personal Finance Example Consider two scenarios: Scenario 1—Certainty A major art gallery has contracted to buy the painting for $85,000 at the end of 5 years. Because this is considered a certain situation, Celia views this asset as “money in the bank.” She thus would use the prevailing risk-free rate of 3% as the required return when calculating the value of the painting. Oil well Expect to receive cash flow of $2,000 at the end of year 1, $4,000 at the end of year 2, and $10,000 at the end of year 4, when the well is to be sold. Scenario 2—High Risk The values of original paintings by this artist have fluctuated widely over the past 10 years. Although Celia expects to be able to sell the painting for $85,000, she realizes that its sale price in 5 years could range between $30,000 and $140,000. Because of the high uncertainty surrounding the painting’s value, Celia believes that a 15% required return is appropriate. © 2012 Pearson Education

Basic Valuation Model The value of any asset is the present value of all future cash flows it is expected to provide over the relevant time period. The value of any asset at time zero, V0, can be expressed as where v0 = Value of the asset at time zero CFT cash flow expected at the end of year t r appropriate required return (discount rate) n relevant time period © 2012 Pearson Education

Personal Finance Example In the case of Michaels stock, the annual cash flow is $300, and Celia decides that a 12% discount rate is appropriate for this investment. Therefore, her estimate of the value of Michaels Enterprises stock is $300 ÷ 0.12 = $2,500 Using a 20% required return, Celia estimates the oil well’s value to be Finally, Celia estimates the value of the painting by discount the expected $85,000 lump sum payment in 5 years at 15% $85,000 ÷ (1 + 0.15)5 = $42,260.02 © 2012 Pearson Education

Bond Valuation: Bond Fundamentals As noted earlier, bonds are long-term debt instruments used by businesses and government to raise large sums of money, typically from a diverse group of lenders. Most bonds pay interest semiannually at a stated coupon interest rate, have an initial maturity of 10 to 30 years, and have a par value of $1,000 that must be repaid at maturity. © 2012 Pearson Education

Bond Valuation: Basic Bond Valuation The basic model for the value, B0, of a bond is given by the following equation: Where B0 = value of the bond at time zero I annual interest paid in dollars n number of years to maturity M par value in dollars rd required return on a bond © 2012 Pearson Education

Bond Valuation: Basic Bond Valuation (cont.) Mills Company, a large defense contractor, on January 1, 2007, issued a 10% coupon interest rate, 10-year bond with a $1,000 par value that pays interest semiannually. Investors who buy this bond receive the contractual right to two cash flows: (1) $100 annual interest (10% coupon interest rate  $1,000 par value) distributed as $50 (1/2  $100) at the end of each 6 months, and (2) the $1,000 par value at the end of the tenth year. Assuming that interest on the Mills Company bond issue is paid annually and that the required return is equal to the bond’s coupon interest rate, I = $100, rd = 10%, M = $1,000, and n = 10 years. © 2012 Pearson Education

Bond Valuation: Basic Bond Valuation (cont.) © 2012 Pearson Education

Bond Valuation: Bond Value Behavior In practice, the value of a bond in the marketplace is rarely equal to its par value. Whenever the required return on a bond differs from the bond’s coupon interest rate, the bond’s value will differ from its par value. The required return is likely to differ from the coupon interest rate because either (1) economic conditions have changed, causing a shift in the basic cost of long-term funds, or (2) the firm’s risk has changed. Increases in the basic cost of long-term funds or in risk will raise the required return; decreases in the cost of funds or in risk will lower the required return. © 2012 Pearson Education

Table 6.6 Bond Values for Various Required Returns (Mills Company’s 10% Coupon Interest Rate, 10-Year Maturity, $1,000 Par, January 1, 2010, Issue Paying Annual Interest) © 2012 Pearson Education

Figure 6.4 Bond Values and Required Returns © 2012 Pearson Education

Bond Valuation: Bond Value Behavior (cont.) Interest rate risk is the chance that interest rates will change and thereby change the required return and bond value. Rising rates, which result in decreasing bond values, are of greatest concern. The shorter the amount of time until a bond’s maturity, the less responsive is its market value to a given change in the required return. © 2012 Pearson Education

Figure 6.5 Time to Maturity and Bond Values © 2012 Pearson Education

Yield to Maturity (YTM) The yield to maturity (YTM) is the rate of return that investors earn if they buy a bond at a specific price and hold it until maturity. (Assumes that the issuer makes all scheduled interest and principal payments as promised.) The yield to maturity on a bond with a current price equal to its par value will always equal the coupon interest rate. When the bond value differs from par, the yield to maturity will differ from the coupon interest rate. © 2012 Pearson Education

Personal Finance Example The Mills Company bond, which currently sells for $1,080, has a 10% coupon interest rate and $1,000 par value, pays interest annually, and has 10 years to maturity. What is the bond’s YTM? © 2012 Pearson Education

Yield to Maturity (YTM) (cont.) The Mills Company bond, which currently sells for $1,080, has a 10% coupon interest rate and $1,000 par value, pays interest annually, and has 10 years to maturity. What is the bond’s YTM? $1,080 = $100 x (PVIFAkd,10yrs) + $1,000 x (PVIFkd,10yrs) Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

Yield to Maturity (YTM): Semiannual Interest and Bond Values Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

Yield to Maturity (YTM): Semiannual Interest and Bond Values (cont.) Assuming that the Mills Company bond pays interest semiannually and that the required stated annual return, kd is 12% for similar risk bonds that also pay semiannual interest, substituting these values into Equation 6.8a yields Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

Yield to Maturity (YTM): Semiannual Interest and Bond Values The procedure used to value bonds paying interest semiannually is similar to that shown in Chapter 5 for compounding interest more frequently than annually, except that here we need to find present value instead of future value. It involves Converting annual interest, I, to semiannual interest by dividing I by 2. Converting the number of years to maturity, n, to the number of 6-month periods to maturity by multiplying n by 2. Converting the required stated (rather than effective) annual return for similar-risk bonds that also pay semiannual interest from an annual rate, rd, to a semiannual rate by dividing rd by 2. © 2012 Pearson Education

Coupon Effects on Price Volatility The amount of bond price volatility depends on three basic factors: length of time to maturity risk amount of coupon interest paid by the bond First, we already have seen that the longer the term to maturity, the greater is a bond’s volatility Second, the riskier a bond, the more variable the required return will be, resulting in greater price volatility. Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

Coupon Effects on Price Volatility (cont.) Finally, the amount of coupon interest also impacts a bond’s price volatility. Specifically, the lower the coupon, the greater will be the bond’s volatility, because it will be longer before the investor receives a significant portion of the cash flow from his or her investment. Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

Current Yield The Current Yield measures the annual return to an investor based on the current price. Current = Annual Coupon Interest Yield Current Market Price For example, a 10% coupon bond which is currently selling at $1,150 would have a current yield of: Current = $100 = 8.7% Yield $1,150 Copyright © 2006 Pearson Addison-Wesley. All rights reserved.